E-Thesis 315 views 89 downloads
Quantum spaces arising from weighted circle actions and their non-commutative geometry. / Simon A Fairfax
Swansea University Author: Simon A Fairfax
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Abstract
Introduction The purpose of this thesis is to investigate weighted actions of the circle group U(1) on known quantum spaces. By introducing suitable weights we are able to construct new unexplored quantum spaces which contain the known quantum spaces in the unweighted case. Once we are able to descr...
| Published: |
2013
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| Institution: | Swansea University |
| Degree level: | Doctoral |
| Degree name: | Ph.D |
| URI: | https://cronfa.swan.ac.uk/Record/cronfa42457 |
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| Abstract: |
Introduction The purpose of this thesis is to investigate weighted actions of the circle group U(1) on known quantum spaces. By introducing suitable weights we are able to construct new unexplored quantum spaces which contain the known quantum spaces in the unweighted case. Once we are able to describe the algebraic structure of these new quantum spaces we investigate their quantum geometry. This thesis is split into two main parts with an outlook of open problems attached; the first consists of introductory material, motivation and an overview of quantum groups and their non-commutative geometry. The second part contains the results from research into quantum weighted projective spaces, in particular describes quantum weighted projective spaces, quantum weighted real projective spaces and quantum weighted Heegaard spaces; see [5], [6] and [7]. Finally, some open problems are discusscd, firstly the existence of a differential calculus over the quantum weighted projective spaces. Secondly, the description of higher dimensional quantum weighted projective spaces. One possible approach for interpreting these spaces on the C*-algebra level is by graph algebra theory; the ideas are discussed briefly in the appendices of this thesis. (Abstract shortened by ProQuest.). |
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| Keywords: |
Mathematics. |
| College: |
Faculty of Science and Engineering |